Perpendicular linear graphs | Maths | Quizalize & Oak National Academy

Starter quiz

Which of these statements is true for parallel lines?

If the gradients of two lines are a zero pair, the lines are parallel.

Parallel lines are the same length.

Parallel lines have the same gradient. ✓

Parallel lines have the same $y$ -intercept.

Parallel lines intersect at right angles.
The gradient of this line is ______.

'-1' ✓
The gradient of this line is ______.

$-{4\over 3}$

$-1$

$-{3\over 4}$ ✓

$-{1\over 2}$

$-{1\over 4}$
The equation of the line drawn below is $y =$ ______ $x -1$ .

'3' ✓
$The equation of the line drawn below is <Math>y = -{4\over 5}x +</Math><span class="blank">______</span>.$

The equation of the line drawn below is $y = -{4\over 5}x +$ ______.

'4' ✓
Using Pythagoras' theorem, the length of this line segment is ______ units.

'10' ✓

Exit quiz

Which of these statements best describes perpendicular lines?

Two lines which are always the same distance apart.

Two lines which are reflections of each other in the $y$ -axis.

Two lines which are the same length.

Two lines which intersect at right-angles. ✓

Two lines which never intersect.
Which of these statements is true for perpendicular lines?

Their gradients are a zero pair.

Their gradients are reciprocals of each other.

Their gradients are the same.

Their gradients have a product of -1 ✓

Their gradients have a product of 1.
Which of these diagrams show two lines which are perpendicular?
Which of these statements is a correct use of the phrase 'if and only if' (iff)?

A shape is a rectangle iff it is a square.

A triangle has a right-angle iff Pythagoras' theorem holds. ✓

A number is an integer iff it is positive.

Two lines are perpendicular iff their gradients have a product of -1. ✓
Which of these is an expression for the length of the line AB?

$\sqrt{m^2}$

$1^2+m^2$

$\sqrt{1^2+m^2}$ ✓

$(\sqrt{1^2+m^2})^2$

$1 + m$
Which of these is equivalent to the equation $(m_1 )^2 + (m_2 )^2 + 2 = (m_1 )^2 + (m_2)^2− 2m_1m_2$ ?

$m_1m_2=1$

$2 =− 2m_1m_2$ ✓

$2(m_1 )^2 + 2(m_2 )^2 = 2− 2m_1m_2$

$(m_1 ) + (m_2 ) + 1 = (m_1 ) + (m_2)− m_1m_2$

Worksheet

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Lesson Details

Key learning points

Two lines are perpendicular if they meet at right angles.
The product of the gradients of two perpendicular lines is -1
This can be derived from Pythagoras' theorem.
The product of the gradients of two lines is -1 iff the lines are perpendicular.

Common misconception

Perpendicular lines have to be drawn as a horizontal and vertical pair.

Some pupils may struggle to see that two lines are perpendicular when they are not drawn horizontally and vertically. Drawing this on paper and then rotating the paper will help them see that it is the angle between the lines that matters.

Keywords

Perpendicular - Two lines are perpendicular if they meet at right angles.
Iff - IFF (If and only if) is an implication that goes both ways.